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Intermediate Algebra

Practice Test

Intermediate AlgebraPractice Test

Practice Test

529.

Use the Square Root Property to solve the quadratic equation 3(w+5)2=27.3(w+5)2=27.

530.

Use Completing the Square to solve the quadratic equation a2−8a+7=23.a2−8a+7=23.

531.

Use the Quadratic Formula to solve the quadratic equation 2m2−5m+3=0.2m2−5m+3=0.

Solve the following quadratic equations. Use any method.

532.

2 x ( 3 x − 2 ) − 1 = 0 2 x ( 3 x − 2 ) − 1 = 0

533.

9 4 y 2 − 3 y + 1 = 0 9 4 y 2 − 3 y + 1 = 0

Use the discriminant to determine the number and type of solutions of each quadratic equation.

534.

6 p 2 − 13 p + 7 = 0 6 p 2 − 13 p + 7 = 0

535.

3 q 2 − 10 q + 12 = 0 3 q 2 − 10 q + 12 = 0

Solve each equation.

536.

4 x 4 − 17 x 2 + 4 = 0 4 x 4 − 17 x 2 + 4 = 0

537.

y 2 3 + 2 y 1 3 − 3 = 0 y 2 3 + 2 y 1 3 − 3 = 0

For each parabola, find ⓐ which direction it opens, ⓑ the equation of the axis of symmetry, ⓒ the vertex, ⓓ the x- and y-intercepts, and e) the maximum or minimum value.

538.

y = 3 x 2 + 6 x + 8 y = 3 x 2 + 6 x + 8

539.

y = − x 2 − 8 x + 16 y = − x 2 − 8 x + 16

Graph each quadratic function using intercepts, the vertex, and the equation of the axis of symmetry.

540.

f ( x ) = x 2 + 6 x + 9 f ( x ) = x 2 + 6 x + 9

541.

f ( x ) = −2 x 2 + 8 x + 4 f ( x ) = −2 x 2 + 8 x + 4

In the following exercises, graph each function using transformations.

542.

f ( x ) = ( x + 3 ) 2 + 2 f ( x ) = ( x + 3 ) 2 + 2

543.

f ( x ) = x 2 − 4 x − 1 f ( x ) = x 2 − 4 x − 1

In the following exercises, solve each inequality algebraically and write any solution in interval notation.

544.

x 2 − 6 x − 8 ≤ 0 x 2 − 6 x − 8 ≤ 0

545.

2 x 2 + x − 10 > 0 2 x 2 + x − 10 > 0

Model the situation with a quadratic equation and solve by any method.

546.

Find two consecutive even numbers whose product is 360.

547.

The length of a diagonal of a rectangle is three more than the width. The length of the rectangle is three times the width. Find the length of the diagonal. (Round to the nearest tenth.)

548.

A water balloon is launched upward at the rate of 86 ft/sec. Using the formula h = −16t2 + 86t find how long it will take the balloon to reach the maximum height, and then find the maximum height. Round to the nearest tenth.

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